Bob Bill Bop

Let a=bob, b=bill, and c=bop. We know $1/a+1/b=1/5$ and that $1/b+1/c=1/6$ , and we are trying to find $1/a+1/c=1/x$ . We learn that a=8, so substituting, we find that $1/8+1/b=1/5$ thus b=40/3. Next, substituting for b, we get $3/40+1/c=1/6$ thus c=120/11. Substituting for a and c, we have $1/8+11/120=1/x$ , thus $x=120/26=60/13$ .

Work= rate x time Let A= time of Bob to finish the work B= time of Bill to finish the work C= time of Bop to finish the work X= the number of hours Bob and Bop required to do the job since A is given as 8. We can substitute it to the equation: 5/8+5/B=1 (Bob and Bill) we get B=40/3. Then, 6/B+6/C=1 (Bill and Bop) by substituting the value of B we get C= 120/11 Since we got already the values A, B and C we can conclude that the rate of Bob=1/8 and rate of Bop=120/11 which leads to our final equation: X/8+X/120/11=1 We get X=60/3 (final answer )

my way :)